Stability Analysis of Explicit and Semi-implicit Euler Methods for Solving Stochastic Delay Differential Equations

  • Norhayati RosliEmail author
  • Noor Amalina Nisa Ariffin
  • Yeak Su HoeEmail author
  • Arifah Bahar
Conference paper


This paper dealt with the stability analysis of explicit and semi implicit Euler methods in approximating the solutions of linear stochastic delay differential equations (SDDEs). It has been proved that the methods are convergent with strong order 0.5 and are numerically stable in general mean square (GMS) and mean square (MS) sense for certain conditions. A comparative study of the stability explicit and semi implicit Euler methods in approximating the solutions of SDDEs are performed to visualize the theoretical results. Numerical experiments are conducted by applying both methods to linear SDDEs.


Stochastic delay differential equations Mean square stable Explicit method Implicit method General mean square stable 



We would like to thank the Ministry of Education (MOE) and Research and Innovation Department, Universiti Malaysia Pahang (UMP) for their financial supports through FRGS Vote No: RDU130122 and Internal UMP Grant RDU1703190.


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Faculty of Industrial Sciences & TechnologyUniversiti Malaysia PahangGambangMalaysia
  2. 2.Faculty of Science, Department of Mathematical SciencesUTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Universiti Teknologi MalaysiaJohor BahruMalaysia

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